MODELING WATER EROSION DUE TO OVERLAND-FLOW USING PHYSICAL PRINCIPLES .1. SHEET FLOW

A new model for erosion of plane soil surfaces by water is developed using physical principles. Raindrop impact and overland flow remove soil from the original cohesive soil. Once eroded soil enters overland flow, either as aggregates or primary particles, a significant proportion of it returns to the soil bed, forming a cohesionless deposited layer from which it can be removed again by the same erosion processes. The action of the eroding agents will be divided between eroding the unshielded original cohesive soil and reintroducing sediment from the deposited layer. The theory recognizes that the nature of the surface is modified by the erosion and deposition processes affecting it. Solutions of the governing differential equations describing sediment concentration are developed for two distinct equilibrium cases. The first case, when the deposited layer completely shields the original soil, appears to correspond with what has been previously called a "transport-limited" situation. The second case occurs when such shielding is incomplete, and sediment concentration is affected by the cohesive strength of the soil. The resulting equations for sediment concentration at equilibrium are compared with existing equations. Firstly, the equation for the case where the soil is lacking cohesion is shown to be similar to the semiempirical equation of Yang (1973). Secondly, when the soil is cohesive the slope length relationships are shown to be in good agreement with the universal soil loss equation over a wide range of slope steepness.